Pressure gauge at the top of a vertical oil well registers 140 bars. the oil well is 6000 m deep and filled with natural gas down to a depth of 4700 m and filled with oil (density=700 kg/m3) the rest of the way to the bottom of the well at 15°c. the compressibility factor z=0.80 for natural gas and its molecular weight is 18.9.
determine the pressure at (a) the natural gas-oil interface and at (b) the bottom of the well at 15°c.

Explanation:

(a)  The given data is as follows.

              Pressure on top () = 140 bar =       (as 1 bar = )

              Temperature = = (15 + 273) K = 288 K

         Density of gas =

                              = 0.4548

                                 =

                                 =

Hence, pressure at the natural gas-oil interface is .

(b)   At the bottom of the tank,

                             = 2.206 \times 10^{7} Pa + 700 \times 9.81 \times (6000 - 4700)[/tex]

                             =

                             = 309.8 bar

Hence, at the bottom of the well at pressure is 309.8 bar.